The ancient teachers divided their courses into basic and advanced curricula known in Latin as the trivium and quadrivium, respectively. The trivium comprises grammar, logic and rhetoric; the quadrivium encompasses arithmetic, geometry, music, and astronomy. Geometry – literally, Earth-measure – soon became our favorite path to learning the ancient wisdom.
Geometry holds the center in the ancient training, as engraved above the door of the academy: ‘Let no one ignorant of geometry enter.’ Through a long process of playing with numbers and practicing geometry, the science of measurement came to seem the most accessible area of ancient science. Benoit Mandelbrot, a pioneer of fractal geometry for whom the Mandelbrot set is named, said in a PBS interview that:
... I fell in love with mathematics, and not mathematics in general, but with geometry in its most concrete, sensual form, that part of geometry in which mathematics and the eye meet. The professor was talking about algebra, but I began to see in my mind geometric pictures which fitted this algebra. And once you see pictures, the answer becomes obvious...[1]
Mandelbrot’s ability to see geometric pictures has not come to both of us yet, but like him our friend did look at old figures and succeed in seeing new geometric facts. Thousands of hours of playing with the Pythagorean theorem and the 3-4-5 triangle gave us a fundamental appreciation for the beauty of number. This exercise also gave hints of how decimal and duodecimal interact, with a power of 10 applied to the base not changing its character, while 12 is the secret sauce on the fish that changes everything. The difference between 10 and 12 is the difference between magnitude and proportion.
It also is unclear how much the ancient Greeks knew, partly due to the ‘secret society’ practice of not disclosing the knowledge publicly. It turns out that the system underlying ancient measures puzzled the brightest minds over many centuries. For example, the 3rd century BCE Greek mathematician Eratosthenes, living in Alexandria, Egypt, knew that the Earth had been measured in the distant past.
Any history of science will usually mention his using the angular difference between summer solstice noon sunlight striking Syrene (Aswan) and Alexandria in order to calculate the Earth’s circumference. Historians usually hold up this enterprise as evidence of Eratosthenes’ genius, but the uncertainty of his facts indicates a knowledge once known, but lost or forgotten.
Oliver Sacks in ‘The River of Consciousness’ titles the last chapter ‘Scotoma: Forgetting and Neglect in Science,’ in which he talks about the scientific community losing knowledge, putting the old accepted knowledge down a ‘scotoma’ – literally, a blind spot, or as here, a ‘memory hole’ or gap in consciousness:
Scotoma, surprisingly common in all fields of science... involves a loss of knowledge, a forgetting of insights that once seemed clearly established, and sometimes a regression to less perceptive explanations. What makes an observation or a new idea acceptable, discussable, memorable? What may prevent it from being so, despite its clear importance and value?[2]
Descartes suspected that many of the ancients kept their methods secret because they feared that the simplicity of those methods would make people think less of them as philosophers.
Telescopes and other instruments sitting on satellites outside the Earth’s atmosphere let humankind see new realities in the most distant reaches of space, and even confirm ancient systems. For example, in the early 1990s the Cosmic Background Explorer satellite investigated the cosmic microwave background radiation and allowed NASA scientists to map microwave light in the Earth's direction of motion.
The blueshift and redshift differential indicates that our cosmic neighborhood is clipping through space at about 1/500th the speed of light. If you think of the number of arc seconds in a circle and say that’s how many knots per hour we’re sailing, you would be pretty close to the odometer. APOD published a four-year cosmic microwave background map on April 3, 2022 and asked, ‘Why are we moving so fast? What is out there?’
The great and inimitable oral historian, Studs Terkel, used the stories of everyday people to paint a picture of society’s health, like a doctor taking the temperature of a whole community. By listening to many people from all walks of life, Terkel found a way to make their voices his voice, to show through their words what he saw in America:
Among those I've encountered in the making of this book are... the blue-collar housewife who, after mothering nine, says: "I don't like the word 'dream.' I don't even want to specify it as American. What I'm beginning to understand is there's a human possibility. That's where all the excitement is. If you can be part of that, you're aware and alive. It's not a dream, it's possible. It's everyday stuff.”[3]
The hidden realities of life on Earth have always appealed to us, too, even the realities tucked away within human beings. As Studs Terkel loved everything about Chicago, so our man as a teenager became fascinated with Appalachia. In that long-ago time he would listen to people and imitate their voices, picking up accents and mannerisms from characters like Johnny, a farm manager from Kentucky, or Icy, the family’s babysitter from West Virginia. Imitating those voices was flattery of the hill people, the ‘hillbillies’ – not condescension.
‘The Foxfire Book’ on Appalachian culture gave him directions to build a pedal-powered lathe using a strip of deerskin and a springy sapling. That book and the people themselves helped him know the wisdom in the hills. You can find an ignorant hillbilly, of course. Icy Hines would smoke her Pall Mall straights down to the nub and tell of growing up in the hollows. One day she was puffing away behind her cloud of blue smoke and delivered her verdict on the space program as Jonah watched an Apollo mission blastoff: ‘Fake, like a movie... government conspiracy filmed in the desert out in Nevada.’
Upon returning to the United States after a long absence, our man found delight in rediscovering some authentic American voices that had been less accessible overseas. One such was Wendell Berry, the Kentucky poet, farmer and writer. Reading him again was like meeting an old friend after many years. In ‘Life is a Miracle’, mainly a diatribe against one pompous author, a frustrated Berry offers this observation:
Science has to do, famously, with theory. ‘Theory,’ at root, is related to the word theater’; it has to do with watching, with observation. A scientific theory is an aid to observation. It involves assumptions that appear to be consistent with known facts. It is not proven; it is useful because it may lead to evidence or to proofs.[4]
If you give a slight twist to one single-atom-thick graphene screen overlaying another one, the material achieves superconductivity, which is when electrons pair up and start to flow together like a wave. A photo of eagle rays swimming side by side illustrates a similar phenomenon with animals. When those two ravens swooped across my path flying wingtip to wingtip, their mating season play, the connectedness of their electrons immediately transformed my state of charge, from wrapped up in my mundane worries to tingling with pleasure at the beauty of life.
In superconductivity, electrons flow freely without any resistance. These subatomic particles carry negative electric charges and power everything from a smartphone to a skyscraper. A team of researchers at Princeton University reported in October 2021 that when the superconducting state ceases, the electrons appear to retain some correlation, a situation that manifests when there is roughly a threshold energy for removing electrons from the sample.
It’s impossible for the average person to read anything written by physicists without having to look up terms to understand what they are talking about. Wikipedia says that ‘in particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide.’
Physicists call this threshold energy a ‘pseudo-gap,’ and say its origin has been a mystery for more than 20 years. In normal circumstances, electrons behave erratically, bumping against each other in a manner that loses energy. In this state the electrons not only do not lose energy, but they also display many novel quantum properties, the researchers reported in Nature. The article says that the emergence of superconductivity in ‘magic-angle twisted bilayer graphene’ raises the possibility that its pairing mechanism is distinct from that of conventional superconductors, and that superconductivity persists even when the electrostatic interactions between electric charges are partially screened.
‘One possibility is that electrons are still somewhat paired together even though the sample is not superconducting,’ said one of the paper’s coauthors. Another possibility is that some other form of collective electronic state must first form before superconductivity can occur. Championship teammates meeting decades after their victory still share a special bond, even if they no longer play the game, which helps illustrate how electrons could ‘remember’ their pairing.
Scholar Joseph Campbell explored the same theme in mythology by finding similarities in creation myths among cultures all over the world. On the aware side, French Jesuit priest and paleontologist Pierre Teilhard de Chardin a hundred years ago helped develop the idea of a collective consciousness, the noösphere, which he said was consistent with 2,000 years of Christian theology. The idea that we are all connected is a day and a half older than the hills.
Pope Benedict XVI in 2009 invoked the noösphere, ‘in which spirit and its understanding embrace the whole and are blended into a kind of living organism.’ Either way, the similarities to high-temperature superconducting materials, as well as how the electrons pair, ‘can't be all a coincidence,’ Princeton physics professor Ali Yazdani said in an article. The magic angle is 1.1 degrees in the case of the superconducting graphene. That’s a concrete fact, but how one feels about the science is subjective.
Vladimir Nabokov opens his autobiography, ‘Speak, Memory’, with this line: ‘The cradle rocks above an abyss, and common sense tells us that our existence is but a brief crack of light between two eternities of darkness.’ Our intuition suggests the opposite. Young children glow with the aura of eternal truth, which parents and teachers tend to make fade. Most people struggle to discover and understand things everyone seems to have known as a matter of collective consciousness in their stardust lives, like the electrons still being ‘somewhat’ connected.
Prepare by way of pilot training. You imagine that if flying an airplane in clouds or in darkness you will be able to perceive up from down, right-side up from upside down, but you will not. How many beginner pilots crash under the delusion that their physical senses must be true? Too many pilots die letting their inner ear override reality, whether or not they know how to read the instruments. Following your intuition can kill you, but then again it might be just what you need. What to do?
An artist can help solve such a conundrum. Conceptual artist Sol LeWitt in 2007 created his last project, ‘Bars of Colors within Squares (MIT),’ a terrazzo floor installed at the Massachusetts Institute of Technology. The school put out a brochure quoting LeWitt from nearly four decades earlier: ‘One should be intelligent enough to know when not to be too intellectual... Conceptual artists are mystics rather than rationalists. They leap to conclusions that logic cannot reach.’[5]
Jonah’s visit to the Guggenheim Bilbao in June 2000 coincided with the prep work on a LeWitt installation. Frank Gehry’s masterpiece of architecture impressed him more than any other building he’d ever seen, but he dismissed the artist-technicians installing LeWitt’s design as mere pawns in a high-class scam. Jonah’s negative attitude stemmed from a combination of ignorance and jealousy, he knowing at the time nothing about conceptual art and struggling to make a magazine in Istanbul turn a profit.
A dab of grace and art history had already imbued him with the sacred trust of art and beauty and life. Study did not convert him to an admirer of the conceptual art so much as the milk of human kindness in the man himself. He chanced to know Sol LeWitt slightly as part of the expatriate circle in Spoleto, Italy, once seeing him at an art exhibit taking time to help a young artist get ahead in the world.
One year after seeing Bilbao, Jonah arrived in Spoleto from Istanbul to visit his father and stepmother. He went straight from the train station to the LeWitt home for a party celebrating the finale of the Festival dei Due Mondi, a music and opera festival held each summer since 1958. Their house overlooked the field where the fireworks team launch the exploding shells.
He arrived early and Sol said, ‘You don’t have any home in America, so Spoleto is like your ancestral home now,’ a warm and generous insight after his day-long journey from the Bosporus. Sol’s wife, Carol, sat him down at the kitchen table with their young daughters and asked Jonah everything about his life, which she said would help broaden the girls’ experience.
Later that evening, as Jonah stood on the terrace watching the fireworks, Sol sidled up and said he was jealous of him being out there in the world, publishing a magazine in Istanbul, that sometimes he wished he had been more adventurous in his youth. Well, of course this made Jonah feel better about both himself and the man – anyone so kind must be sincere in his art.
That’s how his own tawdry vanity helped him appreciate a great artist’s work. Only years later, a decade after the artist’s death, did Sol’s thoughts about not being too intellectual come to show Jonah how they were brothers on the road of spiritual observation and testimony.
Speaking of ancestral homes, Jonah only learned by chance why he felt equally at ease standing on the wharf in Istanbul or in front of the subway entrance at 72nd and Broadway in New York. Walking through a neighborhood near Sisli, Istanbul in 1997, newly returned from exile in Italy, Jonah explored the side streets on his way to visit a friend. An old couple ahead of him walked through an iron gate, behind which he glimpsed the smallest synagogue he’d ever seen.
His friend in the neighborhood, a tour guide and local history buff, told him this was the Khazar synagogue, belonging to a group of Jewish Turks who did not recognize the Sephardic rabbi in Istanbul as their spiritual authority. These Jews came from an area north of the Caspian Sea. Jonah decided to research these mysterious residents. Books at the British Council library pulled him through medieval times into ancient history. A website, Khazaria.com, proved to be a helpful source.
Jews settled in Anatolia as much as two millennia before the migration of Sephardic Jews. Archaeologists working in the Aegean region have uncovered ruins of Jewish settlements from the 4th century BCE. The historian Josephus Flavius relates that Aristotle ‘met Jewish people with whom he exchanged views during his trip across Asia Minor.’
A bronze column found in Ankara lists various rights the Emperor Augustus accorded the Jews of Asia Minor. As the Jews would discover time and again in their long diaspora, 'rights' granted by one emperor can be denied by another. Jews forced to emigrate by the emperor of Byzantium came to the Khazar country, the Turkic Jewish kingdom of Khazaria gave its name to the Caspian Sea in Turkish, Arabic and Persian.
The Khazars spoke Oguz Turkish – a distinct branch of Altaic – and were easygoing with religion. The kings adopted Judaism in the time of Harun al Rashid, in the 8th Century CE. Khazaria enjoyed independence from the fifth through the eleventh centuries and influenced cultures from Europe to India and China. Its borders stretched from Budapest to western Uzbekistan. Khazar rulers tolerated Christian Greeks, pagan Slavs and Muslim Turks, though Islam in its first centuries could not spread to Europe though Central Asia because of Khazaria blocking its way. Muslim Arabs went to Europe the other way round and enriched Sicily and Spain instead.
With Russian conquests in the 10th century, many Khazars fled westward into eastern and central Europe. Some of these have been referred to as Kuzari or Kusar, meaning people from the big lake, or Caspian Sea. At the time of Jonah’s research only 100 Jewish Turks remained in Istanbul, though there were 26,000 Turkish Jews. Often referred to as a belligerent people, Khazars may have chosen Judaism as a way of rejecting Islam and Christianity at the same time.
Perhaps they felt the older monotheistic faith closer to their own Tangri roots. The profession of the Jewish faith came near the end of the Khazarian kingdom, but the Hebrew love of learning led the Khazars to record documents that today serve as the chief source of information on the culture.
These were Turks of the steppe who did not like being closed in by any outsiders. One medieval writer, Druthmar, cited the ‘Gazari’ as being one of the few tribes to outwit Alexander the Great, escaping an encirclement by his troops. Khazars also founded Kiev, with Kui + ev meaning riverbank settlement in Oguz Turkish. Jonah had never been much interested in the distant past of his family, but this information jumped out. His ancestors moved to America from Zurich and he remembered an aunt telling him that the family name meant, ‘people from the village by the lake,’ though no one could figure out how that meaning came from the German language. This might have been an oral history passed down from generation to generation until its origin had been lost.
Does this help explain any of his life, even such a small detail as why he liked the Ukrainian place on 2nd Avenue in New York so much, or why he immediately felt at home in Istanbul? It’s inspiring to imagine a distant relation of his sighting Alexander's army from a hillside near the Black Sea and devising a strategy to escape his more powerful foe.
His eldest brother had the classic build of a Turk, with squat legs supporting a strong torso, topped by a head of dark brown hair, deep brown eyes and a big mustache. Jonah would never have learned all this but for noticing a small synagogue in Istanbul and researching the background to discover some obscure Turkic Jewish history.
[1] Benoit Mandelbrot, The Mandelbrot Set - The only video you need to see!, Video, performed by Benoit Mandelbrot (2016; New York: The BitK/YouTube), Video.
[2] Oliver Sacks, The River of Consciousness, (New York: Knopf, 2016) 205.
[3] Studs Terkel, American Dreams, Lost and Found, (New York: W.W. Norton, 1980), xxv.
[4] Wendell Berry, Life is a Miracle; An Essay Against Modern Superstition, (Washington, D.C.: Counterpoint, 2000), 18.
[5] MIT List Visual Arts Center, “Sol LeWitt; Bars of Color within Squares (MIT), 2007,” Public Works (2007), https://listart.mit.edu/sites/default/files/MIT_PW_LeWitt.pdf.